Semi-analytical modelling of fluid flow in unconventional fractured reservoirs including branch-fracture permeability field

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Abstract

Growing demand for energy and unavailability of new viable energy resources have
played a crucial role in the persistent exploitation of unconventional resources through
multistage hydraulic fracturing. Currently, standard modelling approaches idealize a
fractured media as an interplay of several homogeneous continuum of normal diffusive
characteristics. However, evolved branch-fractures generate a space with extreme
heterogeneity around primary fracture plane. The precise characterization of these
branch-fractures is imperative for well performance analysis along with subdiffusive
behaviour of unconventional matrices. This study presents two semi-analytical models
that account for the branch-fracture permeability field and subdiffusion.
The first model, Induced Branch-fracture Subdiffusive Flow model (SIBFF), accounts
for exponential permeability field concept and subdiffusive transport behaviour
of matrices. Compared to the earlier analytical models, the SIBFF model accounts
for more comprehensive transport mechanisms and medium properties. The other
model, Fractal Branch-fracture model, couples fractal porosity/permeability distribution
of branch-fracture and subdiffusion to account for more detailed description of
stimulated reservoir volume (SRV) and unfractured inner region.
The wellbore pressure solution is derived by discretizing the reservoir into several
flow regions and imposing both flux and pressure continuity at the interface between
contiguous segments. The inclusion of permeability field and fractional flux law introduces
important complexities to the mathematical model that are carefully resolved
by implementing Bessel functions and Laplace transformation (LT). Finally, the solution
is inverted to time domain using Gaver-Wynn-Rho (GWR) algorithm. This
study also assessed the applicability of four numerical inversion methods and found
GWR method more suitable and predictive.
The sensitivity of important model parameters is presented. Results were verified
analytically and validated against Niobrara and Eagleford field data. It is shown that
the models could be implemented to quantify the efficiency of a stimulation job, to
decide on the necessity of re-fracturing a formation and to analyze horizontal well
performance with better predictive capability. The proposed models could further be
employed to characterize different flow regimes for unconventional reservoirs.